# Bethe state norms for the Heisenberg spin chain in the scaling limit

## TL;DR

This paper investigates the norms of Bethe states in the critical Heisenberg spin chain using the ODE/IQFT correspondence, leading to conjectures about their scaling behavior and clarifying the role of Hermitian structures in integrability.

## Contribution

It introduces conjectures on the scaling behavior of Bethe state norms and clarifies the role of Hermitian structures in the integrable framework of the Heisenberg chain.

## Key findings

- Formulated conjectures on norm scaling behavior
- Clarified the role of Hermitian structures in integrability
- Combined analytical and numerical approaches

## Abstract

In this paper we discuss the norms of the Bethe states for the spin one-half Heisenberg chain in the critical regime. Our analysis is based on the ODE/IQFT correspondence. Together with numerical work, this has lead us to formulate a set of conjectures concerning the scaling behavior of the norms. Also, we clarify the role of the different Hermitian structures associated with the integrable structure studied in the series of works of Bazhanov, Lukyanov and Zamolodchikov in the mid nineties.